homogeneous linear differential equation

is called
homogeneous (http://planetmath.org/HomogeneousLinearDifferentialEquation)
iff b⁢(x)≡0. If b⁢(x)≢0,
the equation (1) is inhomogeneous.
If (1) is homogeneous (http://planetmath.org/HomogeneousLinearDifferentialEquation),
then the sum of any solutions is a solution and any solution
multiplied by a constant is a solution.